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A136688 Triangular sequence of q-Fibonacci polynomials for s=2: F(x,n)=x*F(x,n-1)+s*F(x,n-2). 2
1, 0, 1, 2, 0, 1, 0, 4, 0, 1, 4, 0, 6, 0, 1, 0, 12, 0, 8, 0, 1, 8, 0, 24, 0, 10, 0, 1, 0, 32, 0, 40, 0, 12, 0, 1, 16, 0, 80, 0, 60, 0, 14, 0, 1, 0, 80, 0, 160, 0, 84, 0, 16, 0, 1, 32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1, 0, 192, 0, 560, 0, 448, 0, 144, 0, 20 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums are: 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, ... = A001045(n).

Riordan array (1/(1-2x^2),x/(1-2x^2)). - Paul Barry, Jun 18 2008

Diagonal sums are 1,0,3,0,9,... with g.f. 1/(1-3x^2). - Paul Barry, Jun 18 2008

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..500

J. Cigler, q-Fibonacci polynomials, Fibonacci Quarterly 41 (2003) 31-40.

FORMULA

s=2:F(x,0)=0;F(x,1)=1; F(x,n)=x*F(x,n-1)+s*F(x,n-2)

EXAMPLE

1,

0, 1,

2, 0, 1,

0, 4, 0, 1,

4, 0, 6, 0, 1,

0, 12, 0, 8, 0, 1,

8, 0, 24, 0, 10, 0, 1,

0, 32, 0, 40, 0, 12, 0, 1,

16, 0, 80, 0, 60, 0, 14, 0, 1,

0, 80, 0, 160, 0, 84, 0, 16, 0, 1,

32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1,

...

MAPLE

A136688 := proc(n) option remember: if(n<=1)then return n: else return x*A136688(n-1)+2*A136688(n-2): fi: end:

seq(seq(coeff(A136688(n), x, m), m=0..n-1), n=1..10); # Nathaniel Johnston, Apr 27 2011

MATHEMATICA

Clear[F, x, s, n] s = 2; F[x, 0] = 0; F[x, 1] = 1; F[x_, n_] := F[x, n] = x*F[x, n - 1] + s*F[x, n - 2]; Table[ExpandAll[F[x, n]], {n, 1, 11}]; a = Table[CoefficientList[F[x, n], x], {n, 1, 11}]; Flatten[a]

CROSSREFS

Cf. A136689, A136705.

Sequence in context: A073430 A053389 A202328 * A131321 A111959 A110109

Adjacent sequences:  A136685 A136686 A136687 * A136689 A136690 A136691

KEYWORD

nonn,easy,tabl

AUTHOR

Roger L. Bagula, Apr 06 2008

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)